Q. 34.7( 3 Votes )

The mean of the f

Answer :

This is a grouped frequency distribution.


To find x and y, we’ll need to find mean of the following distribution by assumed mean method and equate it to the given mean of the following distribution, 332.


And class size, c = 50.


[ (150 – 100) = (200 – 150) = (250 – 200) = … = (550 – 500) = 50]


This given data is in exclusive type.


So, let’s construct a table finding midpoints and stating frequencies.



So now, we have


fiui = -130 – 3x


And fi = 146 + x + y = 200


Mean is given by



[given, mean = 332 and using the values from the table]




43 × 4 = 130 + 3x


172 = 130 + 3x


3x = 172 – 130


3x = 42



x = 14 …(i)


Since, there are 200 observations.


Sum of frequencies = 200 [Sum of frequencies depict total number of observation]


fi = 200


146 + x + y = 200


x + y = 200 – 146


x + y = 54 …(ii)


Putting the value of x from equation (i) into equation (ii), we get


x + y = 54


14 + y = 54


y = 54 – 14


y = 40


Thus, the missing frequencies are x = 14 and y = 40.


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